First Principle Thermodynamic and Dynamic Simulations for Dense Quantum Plasmas

Abstract

We present a detailed analysis of temperature-dependent effective quantum pair potentials. These potentials are derived from first-principle path integral Monte Carlo simulations and are accurate even at strong coupling and partial ionization. They can be efficiently used in molecular-dynamics (MD) simulations to obtain accurate thermodynamic and dynamic properties of strongly coupled hydrogen down to the temperatures of about 60 000 K. Furthermore, using spin-dependent pair potentials, dynamic structure factors and spin-density correlation functions were calculated for different values of coupling and degeneracy.

The method of effective potentials in the quantum-statistical theory of plasmas

“…We mentioned already the pioneering work of Hansen et al [11]. More recent MD simulations have shown that the use of Kelbg-type effective potentials provides good thermodynamic functions, correlation functions, microfield distributions and, to some extent, also non-equilibrium properties [20][21][22][23][24][25][26].…”

Quantum Hydrodynamics

“…It has many properties characteristic of nonlinear waves, especially localized modes and solitons, and beam-driven waves and instabilities. The NLS equation and its variants describe nonlinear physical systems appearing in a wide spectrum of problems in (quantum) plasmas 21 and other fields, for example, in fluids and water waves, ultrafast transmission systems, condensed matter systems, and so on. NLS contains an additional nonlinear term in the Schrödinger equation responsible for the nonlinear effects.…”

“…(1.28) also facilitates the verification of numerical solvers and aids in the stability analysis. Discrete nonlinear Schrödinger (DNLS) equations are also important in discrete lattice models in nonlinear optics, 21 always assuming that the applicability conditions of QHD are fulfilled. condensed matter and trapped Bose-Einstein condensates where a numerical evaluation is straightforward using e.g.…”

“…From the linearized QHD equations they obtained for the inverse dielectric function 21 The effective mass takes into account medium effects for the case of electrons in condensated matter systems. Here we will focus on electrons in a hydrogen plasma where m * coincides with the free electron mass.…”

“…At the same time, for fermions, it is limited to small systems, due to the so-called fermion sign problem. Equilibrium properties of correlated quantum systems can also be described by quantum molecular dynamics (QMD) techniques which include, for instance, the Wigner function QMD [20], or classical MD with quantum and spin effects included via effective quantum potentials [21]. For equilibrium solutions, theories like the random phase approximation (RPA) and quantum mechanical modeling by density functional theory (DFT) [22,23] are also very successful.…”